I want to test whether two objects are similar or not. I have multivariate samples like this:

Object1: X1, Y1, Z1, etc.

Object2: X2, Y2, Z2, etc.

Each letter is a variable, where same letter means same type of measurement. Variables do not follow a specific distribution (nonparametric) and they are iid. I have about 70k measurements per variable.

I need to compare objects (with all their variables and measurements, or some of them).
I thought about performing a Permutational MANOVA, but I am not sure if it is the best option. A multivariate kolmogorov-smirnov for two samples would be also good, but as far as I read it is not easy.